As coordinator of the AlgPoW service, I am happy to inform allteachers who are using my problems with their students, that I havejust add some significant new material to my Guidelines for WritingPoW Answers page. The most important item concerns my policyregarding the use of guess-and-check as the primary strategy forsolving the problems. It says:

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Use of Guess-and-Check Procedure

In general, the method of "guess-and-check" is not allowed in AlgPoWas your primary strategy to solve the problem. This is not sayingguess-and-check is not a good way to solve problems. In fact, it isoften a good way to start to understand a problem, and thereforerecommended for that. But for most of our problems, you must definevariables or unknowns, then form equations to solve by logical steps.

Historically, it was the main way that problems were solved. But asadvances were made in symbolic notation, mathematicians moved awayfrom it and toward the more efficient and time-saving methods ofstep-by-step manipulations on equations.

One of my mentors told me that he advises students in the followingway:

"Guess and check is a valid problem-solving approach. However, italso one of the most difficult to explain. If you are going to useguess and check, you must list every guess, along with the reason thatyou know the answer is incorrect. You also must explain why you knowyour final answer is the only possible answer. In all, a pretty longprocess; however, since this is the Algebra Problem of the Week, youmight want to try algebra. Please read the "Guidelines for Writing POWAnswers." The link is at the bottom of the problem."

I hope this makes things more clear for everybody. I would like torecommend that copies of the "new and improved" Guidelines page bemade for distribution to students. Some teachers have already donethis, but now there is more information than originally.